Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
402 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 101 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×#63449 | C2 | semidirect |
| 4. #11720526 | C2 | semidirect |
| 6. #11720276 | C2 | semidirect |
| 7. C3⋊C8×Dic9 | C2 | semidirect |
| 21. #88423 | C4 | semidirect |
| 31. #63449 | D3 | semidirect |
| 47. C3×Dic18 | C2×C4 | semidirect |
| 49. C3⋊(C9⋊C8) | C2×C4 | semidirect |
| 90. C3×Dic9 | SD16 | semidirect |
| 134. Dic18 | C4×D3 | semidirect |
| 196. Dic9 | #215 | semidirect |
| 204. C3×C9 | C4×SD16 | semidirect |
| 289. C9 | C4×#215 | semidirect |
| 327. C3 | #10588438 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#63449 | 2 |
| D12×Dic9 | 2 |
| C2×#88423 | 2 |
| #11720526 | 2 |
| C9×#809 | 2 |
| #11720276 | 2 |
| C3⋊C8×Dic9 | 2 |
| #10590453 | 3 |
| #10588438 | 3 |